Objective: Polar coordinate system. Coordinate conversion.

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Presentation transcript:

Objective: Polar coordinate system. Coordinate conversion. Warm up Prove the half angle identity for Tangent.

Polar coordinate system: If r > 0, then P is on the terminal side of . If r < 0, then P is on the terminal side of .

Polar coordinate system:

Example 1 Plot the points with the given polar coordinates. A B C D E

Coordinate Conversion: Rectangular to Polar: Polar to rectangular: Proof:

Example 2 Convert from polar to rectangular coordinates. a. b Example 2 Convert from polar to rectangular coordinates. a. b. Example 3 Convert from rectangular to polar coordinates.

b. c. Finding all polar coordinates of a point P. or

Example 4 Find another representation of point in which: a. r is positive and . r is negative and . r is positive and .

Assignment Pg 672 #1-10, 16,18, 20-22, 27, 34, 35, 42, 43.